Question

Write an explicit rule for the following arithmetic sequence: 28, 38, 48, 58,

Answer 1

When you have an arithmetic sequence you can use the next general formula to get the explicit formula:

`a(n)=a(1)+d(n-1)`

Where a(1) is the first term in the sequence, d is the difference between each term in the sequence, and n is the nth term

You have the sequence: 28,38,48,58

The difference in this sequence is d=10

The first term is: a(1)=28

Then:

`a(n)=28+10(n-1)`
`a(n)=28+10n-10`
`a(n)=18+10n`Then, the explicit rule for the given arithmetic sequence is: a(n)=18+10n